brdf_microfacet — SPECULAR reflectance op

• Data kinds: normalmap → image2d

• Call: import fullseye as fs; fs.ledger.brdf_microfacet(normals, light=(0.0, 0.0, 1.0), view=(0.0, 0.0, 1.0), roughness=0.3, f0=0.04) (implementation को सीधे call करना हो तो import specularity; specularity.brdf_microfacet(normals, light=(0.0, 0.0, 1.0), view=(0.0, 0.0, 1.0), roughness=0.3, f0=0.04), registry से लेना हो तो opsspecular.get("brdf_microfacet"))

उपयोग

GGX / Trowbridge-Reitz microfacet specular BRDF। → (H, W), इकाई 1/sr।

> नीचे का विस्तृत विवरण मूल text में है — सारांश और headings का अनुवाद हो चुका है।

f_s = D * G * F / (4 (n.l) (n.v)) with

• D the Trowbridge-Reitz (1975) / GGX normal distribution, a^2 / (pi * ((n.h)^2 (a^2 - 1) + 1)^2) for a = roughness^2, which integrates to 1 against (n.h) dw over the hemisphere — measured by 20000-point midpoint quadrature in tests/test_specularity.py at relative errors 3.2e-07, 6.3e-08 and 4.0e-09 for roughness 0.2, 0.3 and 0.6, all of it quadrature error (the 200000-point rule gives 3.2e-09, 6.3e-10, 4.0e-11, exactly the 100x a midpoint rule predicts);

• G the separable Smith (1967) masking-shadowing term with the GGX lambda;

• F Schlick's (1994) Fresnel approximation, f0 + (1 - f0) (1 - v.h)^5. *f0* is the normal-incidence reflectance:

about 0.04 for common dielectrics, 0.5 to 1.0 for metals. When the exact

Fresnel curve matters, use match3d.fresnel_reflectance instead — this

is the approximation the microfacet literature specifies, and it is named

rather than hidden.

Exact ground truth it reproduces: at normal incidence with light, view and normal aligned, every geometric factor is 1 and the value collapses to f0 / (4 pi roughness^4) in closed form — reproduced bit for bit at roughness 0.3, 0.5 and 1.0 and to 3.3e-16 relative at roughness 0.1, which took rewriting the GGX denominator to avoid a cancellation (see the comment at the code; the textbook arrangement was off by 2.2e-13 relative at the peak). The lobe is reciprocal in light and view to machine precision (measured 1.7e-16), and its maximum sits at the half-vector.

roughness is the perceptual parameter, squared once to reach the GGX alpha — the convention that makes a linear slider feel linear. A perfectly smooth surface (roughness = 0) is a delta function, not a finite BRDF, so it is refused rather than returned as an infinity.

Raises ValueError: geometry problems as in brdf_blinn_phong; *roughness* outside (0, 1]; *f0* outside [0, 1].

उपयोग की विस्तृत guide

• specular_photometric family guide

संदर्भ (sample data, साहित्य)

• Sample data catalog (DL URL / license) — 2-D के लिए skimage.data (BSD/public) + synthetic, 3-D के लिए real data sources (Stanford/PDS आदि) के DL URL।

• Operators का स्रोत और संदर्भ — इस op family के मूल research/methods के स्रोत।

• Algorithm का मानक स्रोत (लेखक, वर्ष) और उपयोग ऊपर की family usage guide में दिए गए हैं।

चलाए जा सकने वाले उदाहरण (verified samples जो सच में यह op call करते हैं)

• poc_solder_fillet_aoi — py -3.11 examples/poc_solder_fillet_aoi.py

• specular_photometric — py -3.11 examples/specular_photometric.py

वे अगले ops जिनसे type जुड़ता है (image2d को input के रूप में लेते हैं)

polarization_render

इसी category के (reflectance)

brdf_blinn_phong · dichromatic_render


*Provenance: specularity.py — SPECULAR operator registry. यह per-op note tools/opdocs.py md से अपने-आप generate होता है (हाथ से edit न करें)।*

© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.